Given that z_1 = R_1 + R + jωL ; z_2 = R_2 ; z_3 = (1/(jωC_3 )) and z_4 = R_4 + (1/(jωC_4 )) and also that z_1 z_3 = z_2 z_4 , express R and L in terms of the real constants R_1 , R_2 , R_4 , C_3 and C_4 Answer: R = ((R_2 C_3 − R_1 C_4 )/C_4 ) , L = R_2 R_4 C


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Question Number 51250 by Tawa1 last updated on 25/Dec/18

$Given that z_{1} = R_{1} + R + j ω L; z_{2} = R_{2}; z_{3} = \frac{1}{j ω C_{3}}$ $and z_{4} = R_{4} + \frac{1}{j ω C_{4}} and also that z_{1} z_{3} = z_{2} z_{4}, express$ $R and L in terms of the real constants R_{1}, R_{2}, R_{4}, C_{3} and C_{4}$ $Answer : R = \frac{R_{2} C_{3} - R_{1} C_{4}}{C_{4}}, L = R_{2} R_{4} C_{3}$
	Answered by tanmay.chaudhury50@gmail.com last updated on 25/Dec/18

	$z_{1} z_{3} = z_{2} z_{4}$ $(R_{1} + R + j w L) \frac{1}{{j w C}_{3}} = R_{2} (R_{4} + \frac{1}{{j w C}_{4}})$ $c o m p a r i n g r e a l a n d i m a g i n a r y p a r t$ $\frac{R_{1} + R}{{j w C}_{3}} = \frac{R_{2}}{{j w C}_{4}}$ $R_{1} C_{4} + {R C}_{4} = R_{2} C_{3}$ $R = \frac{R_{2} C_{3} - R_{1} C_{4}}{C_{4}}$ $\frac{L}{C_{3}} = R_{2} R_{4} [L = C_{3} R_{2} R_{4}$
	Commented by Tawa1 last updated on 25/Dec/18

	$God bless you sir$
	Commented by tanmay.chaudhury50@gmail.com last updated on 26/Dec/18

	$t h a n k y o u . . .$
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